Line l contains points (2,4). Point P has coordinates (1,1). Find the distance from P to l

Mathematics

1 answer:

lina2011 [118]3 years ago

4 0

Answer:

Step-by-step explanation:

$(2,4)=(x_1,y_1)\\(5,1,)=(x_2,y_2)\\\\d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\\\d==\sqrt{\left(5-2\right)^2+\left(1-4\right)^2}\\\\d=\sqrt{3^2+3^2}\\\\d=\sqrt{3^2\times\:2}\\\\d=\sqrt{2}\sqrt{3^2}\\\\\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0\\\\\sqrt{3^2}=3\\d =3\sqrt{2}\\$

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Shauna spent $175 on a pair of shoes.She spent 1/9 of the remaining money on a shirt.If he still had 4/7of his moneyleft,how muc

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Answer:

$490

Step-by-step explanation:

Shauna spent $175 on a pair of shoes.

She spent 1/9 of the remaining money on a shirt.

If he still had 4/7 of his money left,how much did he have at first ?

Solution:

Let at first, Shauna have = $x$

Money spent on a pair of shoes = $175

Remaining money = $x-175$

<u>As she spent 1/9 of the remaining money on a shirt.</u>

Money spent on shirt = $\frac{1}{9} \times(x-175)=\frac{x}{9} -\frac{175}{9}$

As he still had $\frac{4}{7}$ of his money left:-

Money left = $\frac{4}{7}\ of\ his\ money=\frac{4x}{7}$

Money left with Shauna = Total money, she had at first -(Money spent on a pair of shoes + Money spent on shirt )

$\frac{4x}{7} =x-(175+{\frac{x}{9} -\frac{175}{9} )\\\\\\$

$\frac{4x}{7} =x-(\frac{175}{1} -\frac{175}{9} +\frac{x}{9} )\\\\ \frac{4x}{7} =x-(\frac{1575-175}{9} +\frac{x}{9} )\\\\ \frac{4x}{7}=x-(\frac{1400}{9} +\frac{x}{9} )\\ \\ \frac{4x}{7}=x-\frac{1400}{9} -\frac{x}{9}$